Lesson 7 – Momentum & Collisions

Stage 1: Intermediate Complete Notes
Page 6 – One-Dimensional Collision Problems

This page focuses on solving numerical problems involving one-dimensional collisions using conservation of momentum and coefficient of restitution.

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1️⃣ Standard Method to Solve Collision Problems

Step 1: Choose direction of motion as positive
Step 2: Apply conservation of momentum
Step 3: Use coefficient of restitution equation
Step 4: Solve the two equations for final velocities

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2️⃣ Solved Problem 1

A ball of mass 2 kg moving with velocity 6 m/s collides head-on elastically with a stationary ball of mass 4 kg. Find the velocities after collision.

Given:
m₁ = 2 kg, u₁ = 6 m/s
m₂ = 4 kg, u₂ = 0
e = 1 (elastic collision)

Solution:

Conservation of momentum:

2×6 + 4×0 = 2v₁ + 4v₂ → 12 = 2v₁ + 4v₂

Coefficient of restitution:

v₂ − v₁ = 6

Solving equations:

v₁ = −2 m/s
v₂ = 4 m/s

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3️⃣ Solved Problem 2

A bullet of mass 10 g is fired into a stationary wooden block of mass 990 g and embeds itself in it. Find the common velocity after collision if bullet speed is 500 m/s.

Given:
m₁ = 0.01 kg, u₁ = 500 m/s
m₂ = 0.99 kg, u₂ = 0
e = 0 (perfectly inelastic)

Solution:

(0.01×500) + (0.99×0) = (1)v

v = 5 m/s

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4️⃣ Important Exam Observations

✔ Always write momentum equation first
✔ Use e only after momentum equation
✔ Negative velocity indicates reversal of direction

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5️⃣ Common Mistakes to Avoid

❌ Ignoring sign convention
❌ Forgetting unit conversion
❌ Using energy conservation in inelastic collisions

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📌 Page 6 Summary

✔ Two equations needed: momentum + e
✔ Negative velocity shows direction change
✔ Perfectly inelastic → common velocity
✔ Highly scoring topic in exams

👉 Next page: Two-Dimensional Collisions (Conceptual Introduction)